JournalscmhVol. 82 , No. 4DOI 10.4171/cmh/108

Injections of Artin groups

  • Robert Bell

    Michigan State University, East Lansing, United States
  • Dan Margalit

    Georgia Institute of Technology, Atlanta, United States
Injections of Artin groups cover


We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a sphere with at least 5 punctures. In particular, we show that any injective homomorphism between these groups is given by a homeomorphism of a punctured sphere together with a map to the integers. The technique, following Ivanov, is to prove that every superinjective map of the curve complex of a sphere with at least 5 punctures is induced by a homeomorphism. We also determine the automorphism group of the pure braid group on at least 4 strands.